Matter-wave interferometry has been performed with helium atoms in high Rydberg states.In the experiments the atoms were prepared in coherent superpositions of Rydberg states with different electric dipole moments. Upon the application of an inhomogeneous electric field, the different forces on these internal state components resulted in the generation of coherent superpositions of momentum states. Using a sequence of microwave and electric field gradient pulses the internal Rydberg states were entangled with the momentum states associated with the external motion of these matter waves. Under these conditions matter-wave interference was observed by monitoring the populations of the Rydberg states as the magnitudes and durations of the pulsed electric field gradients were adjusted. The results of the experiments have been compared to, and are in excellent quantitative agreement with, matter-wave interference patterns calculated for the corresponding pulse sequences. For the Rydberg states used, the spatial extent of the Rydberg electron wavefunction was ∼ 320 nm. Matter-wave interferometry with such giant atoms is of interest in the exploration of the boundary between quantum and classical mechanics. The results presented also open new possibilities for measurements of the acceleration of Rydberg positronium or antihydrogen atoms in the Earth's gravitational field. arXiv:1907.07649v1 [physics.atom-ph] 17 Jul 2019Recently, in a similar vein, coherent momentum splitting of laser cooled rubidium atoms, prepared in chip-based magnetic traps, was demonstrated using pulsed inhomogeneous magnetic fields and a sequence of radio-frequency (RF) pulses to prepare, and coherently manipulate, ground-state Zeeman sublevels [44]. In these experiments a π/2 pulse of RF radiation was first applied to prepare a coherent superposition of sublevels with magnetic dipole moments of equal magnitude but opposite orientation, in a homogeneous background magnetic field. The atoms were then subjected to a pulsed inhomogeneous magnetic field. The forces exerted by this field gradient on each component of the internal-state superposition resulted in the generation of a superposition of momentum states. Spatial interferences between the resulting pairs of matter waves were then observed by state-selective imaging of the atoms